Dimension of <xn,tn|xn-1,tn-1>

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Discussion Overview

The discussion revolves around the dimensional analysis of the expression as presented in Sakurai's "Modern Quantum Mechanics." Participants are seeking clarification on why this expression is said to have a dimension of 1/length, exploring the implications of this dimension in the context of quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion regarding the dimension of being 1/length and requests explanations.
  • Another participant suggests that performing a dimensional analysis would yield the result of 1/L, implying a straightforward interpretation.
  • A participant asks for a detailed dimensional analysis to understand why the dimension is 1/length.
  • There is a question regarding the representation of the state vector | x,t ⟩ and its implications for particle localization at a specific position x at time t.
  • Another participant asserts that since the state vector relates to particle localization, they believe the dimension should be length, indicating a potential disagreement on the interpretation of dimensions.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the dimensionality of the expression, with some supporting the idea of 1/length while others argue for a dimension of length based on the state vector's representation.

Contextual Notes

There are unresolved assumptions regarding the definitions and interpretations of the state vector and its dimensional implications, as well as the specifics of the dimensional analysis that some participants are requesting.

einstein1921
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HI! Everyone!I have a problem! I read sakurai's <modern quantum mechanics>.It reads the dimension of <xn,tn|xn-1,tn-1> is 1/length.I DON'T understand!would you like to give me some explanations? thank you!
 
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What don't you understand - it's saying that if you did a dimensional analysis on that thing it would come up with 1/L

Note - you can write in the subscripts in two ways:

<xn,tn|xn-1,tn-1>

or

[itex]\langle x_n , t_n \mid x_{n-1}, t_{n-1} \rangle[/itex]

the second one is best. (assuming you meant the subscripts...)
hit the "quote" button at the bottom of this reply to see what I did.
 
Simon Bridge said:
What don't you understand - it's saying that if you did a dimensional analysis on that thing it would come up with 1/L

Note - you can write in the subscripts in two ways:

<xn,tn|xn-1,tn-1>

or

[itex]\langle x_n , t_n \mid x_{n-1}, t_{n-1} \rangle[/itex]

the second one is best. (assuming you meant the subscripts...)
hit the "quote" button at the bottom of this reply to see what I did.

Thank you ,Simon.I don't understand why the dimension is 1/length.Could you please did a dimensional analysis for me?
 
What does the state vector [itex]| x,t \rangle[/itex] represent?
 
Simon Bridge said:
What does the state vector [itex]| x,t \rangle[/itex] represent?

at time t,particle localize x! I think dimension is length.so I need help. Thank you!
 

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